Quinolone carboxylic acid derivatives are widely used as synthetic antibacterial agents in the medical field. Notwithstanding such usefulness, the derivatives are fraught with therapeutically serious problems due to growing emergence of resistant bacteria, such as MRSA. Even so, quinolone carboxylic acid derivatives exhibit not only excellent capability of killing MRSA but also antibacterial activity against resistant Gram-positive bacteria, thus serving as compounds able to solve various problems involved in resistant bacteria.
In production of a quinolone carboxylic acid derivative; e.g., the quinolone carboxylic acid derivatives shown below, an optically active compound represented by formula (6) is of great importance for the construction of a substituent present at the 7-position thereof (Patent Documents 1 and 2).

Thus far various methods have been known for producing an optically active compound represented by formula (6) (Patent Documents 1, 2, and 3).    [Patent Document 1] WO96/23782    [Patent Document 2] WO2002/40478    [Patent Document 3] WO96/39407